Firstly - Don't panic.
Our son (7 now) at the age of 3 only neded about 4 hours sleep a night never slept through the day. We thought Hyperactive as well.He never slept a full night from he was born and we were told - He will sleep when he gets his own bed/own room/is one /two / three the list goes on.
He only started to sleep when he started playgroup .We came to the conclusion that he needed more stimulus than we could provde for him at home and that he needed a group of friends of his own age to play with to tire him out .
Sounds to me like your kid is ready for the next step - lots of thinking and learning to keep him occupied.
While the doctors are the experts you know your kid better than they do .

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Don't take away the SNC